Osmosis drives the development of a pressure difference of many atmospheres between a dilute
solution and pure solvent with which it is in contact through a semi-permeable membrane. The
educational importance of this paper is that it presents a novel treatment in terms of fluid
mechanics that is quantitative and exact. It is also simple and intuitive, showing vividly how
osmotic pressures are generated and maintained in equilibrium, driven by differential solvent
pressures. The present rigorous analysis using the virial theorem seems unknown and can be easily
understood—and taught—at various different levels. It should be valuable to undergraduates, graduate
students and indeed to the general physicist.